Spie Press Book

This second volume based on Michael Kidger's popular short courses and workshops is aimed at readers already familiar with the concepts presented in Fundamental Optical Design (SPIE Press Vol. PM92). It begins with a sweeping discussion of optimization that is written with the user in mind and continues with a unique look at the role of higher-order aberrations. The book's key feature is its astounding presentation of a wide range of practical design examples, covering such problems as secondary spectrum correction, high numerical aperture designs, lasers, zoom lenses, tilted or decentered optical systems, and price and performance requirements. Each scenario is accompanied by an in-depth discussion that goes well beyond the ray aberration plot, including useful insights into an optical designer's thought processes.

1.2.7 A method of visualizing the problem of optimization in lens design

1.3 Theory of damped least squares (Levenberg-Marquardt)

1.3.1 Use of Lagrange multipliers to control constraints

1.4 Some details of damped least squares as used in lens design

1.4.1 Paraxial (first-order) properties

1.4.2 Seidel and Buchdahl coefficients

1.4.3 Transverse ray or wavefront aberrations

1.4.4 Aberration balancing and choice of weighting factors

1.4.5 Damping

1.4.6 Control of physical constraints

1.4.7 Control of glass boundary conditions

1.4.8 Solves

1.4.9 Lagrange multipliers

1.5 Some reasons for the success of the DLS method

1.6 Experiments with optimization programs

1.6.1 Effect of changing the damping factor

1.6.2 Effect of scaling the parameter changes

1.7 An optimization example

References

Chapter 2 Buchdahl Aberrations

2.1 Third-order coefficients

2.2 Fifth-order coefficients

2.3 Comparison with H. H. Hopkins notation

2.4 Examples

2.4.1 Double Gauss

2.4.2 Shafer lens with zero third and fifth order aberrations

References

Chapter 3 Synthesis of New Lens Design

3.1 Choice of a starting point

3.1.1 Modification of an existing design

3.1.2 Purchase of a competing lens

3.1.3 Analytic solutions

3.1.4 Non-analytic synthesis of new design forms

3.2 Examples

3.2.1 A unit magnification telecentric doublet pair

3.2.2 A simple zoom lens

3.3 The use of catalog components

3.3.1 Singlets

3.3.2 Doublets and triplets

3.3.3 Meniscus and singlets

3.3.4 Field flatteners

3.3.5 Cemented triplets

References

Chapter 4 Lenses for 35-mm Cameras

4.1 The Triplet

4.2 The Tessar

4.3 The Double Gauss (Planar-type)

4.4 The Sonnar

4.5 Wide-angle lenses for rangefinder cameras Zeiss Biogon

4.6 Wide-angle lens for rangefinder camera (Schneider Super-Angulon)

4.7 Winde-angle lenses for SLR cameras

4.8 Telephoto lens

4.9 Long-focus telephoto lens

4.10 Lens for compact "point-and-shoot" camera

4.11 Single lens for disposable cameras

References

Chapter 5 Secondary Spectrum and Apochromats

5.1 Apochromatic doublets

5.2 Apochromatic triplets

5.3 Petzval lenses

5.4 Double Gauss lenses

5.5 Telephoto lenses

5.6 Zoom lenses

5.7 Microscope objectives

5.8 Secondary spectrum correction with normal glasses

5.8.1 Liquids

5.8.2 Diffractive optics

5.9.3 McCarthy-Wynne principle

5.9.4 Schupmann principle

5.9 Transverse secondary spectrum

References

Chapter 6 Lenses for Laser Applications

6.1 Gaussian beams

6.2 Laser beam expanders

6.2.1 Two-lens beam expanders

6.2.3 Three-lens beam expanders

6.3 F-theta lenses

6.4 Lenses for optical disks

6.5 Laser diode collimators

References

Chapter 7 Microscope Objectives

7.1 Classical microscope objectives

7.2 Flat-field microscope objectives

7.3 Oil-immersion objectives

References

Chapter 8 Microlithographic Projection Optics

8.1 Unit-magnification zero-power monocentric systems

8.1.1 Dyson 1x relay

8.1.2 Offner 1x relay

8.1.3 Wynne-Dyson 1x relay

8.1.4 Wynne-Offner 1x relay

8.2 Reduction lenses

8.3 Catadioptric reduction systems

8.4 Catoptric reduction systems

References

Chapter 9 Zoom Lenses

9.1 General principles

9.1.1 Control of chromatic aberration

9.1.2 Field curvature

9.1.3 Minimization of movements

9.2 Two component zooms

9.2.1 Minus-plus plastic disposable zoom

9.2.2 Plus-minus plastic disposable zoom

9.2.3 A typical minus-plus zoom

9.2.4 A typical plus-minus zoom

9.3 Three component zooms

9.3.1 Optical compensation

9.4 Four component zooms

9.5 Zoom relays

9.6 Zoom telescopes

9.7 Zoom "modules"

References

Chapter 10 Decentered and Asymmetric Systems

10.1 General properties of decentered systems

10.2 Coordinate systems

10.3 Interpretation of results

10.4 New axis surface

10.5 Toroids

10.6 Offset surfaces (or off-axis surfaces)

10.7 Convention for mirrors

10.8 Kutter system

10.9 Single parabolic mirror

10.9.1 Alpha rotations

10.9.2 Beta rotations

10.9.3 Alpha and beta rotations

10.10 Scanning systems

10.11 The "active" side of a surface

10.12 X-ray telescopes

10.12.1 WOLTER2 example

10.12.2 WOLTER1 example

Chapter 11 Design for Manufacturability

11.1 Tolerancing

11.2 Simplicity of design

11.3 Airspaces

11.4 Glass components

11.5 Glass choice

11.6 Mirror surfaces

11.7 Redesign for actual "melt" data

11.8 The use of existing tools and testplates

11.9 Selective assembly and adjustment after assembly

11.10 General points

References

Index

Preface

The title of this book originates from Michael Kidger's short courses for SPIE titled
"Intermediate Optical Design." It is a compilation of material from these courses and a
number of similar ones given for Kidger Optics in Australia, Germany, Italy, Sweden,
Singapore, and the UK during the 1990s. It forms the second of two volumes, the first
being Fundamental Optical Design, published by SPIE Press in 2002.

These intermediate level courses were aimed at students and practicing optical
designers who already had a thorough knowledge of geometrical optics and third-order
(Seidel) aberration theory. The courses continued to use the same "Imperial College"
nomenclature and the Sigma optical design program as the basis for the course work. They
were workshops, or master classes, rather than academic discourses or promotional
material for Sigma. In the interests of authenticity and continuity with the first volume, the
same Sigma output format is used here for tables of lens prescriptions, aberration data, and
graphics. This second volume does not review the material in the first volume; the
assumption is that the reader is already familiar with it, preferably having already worked
through the examples in that volume, and is able to refer back to it when needed. The
connections between the two volumes are not often explicit, but rather left for the
perceptive reader to discover as he or she works through these design examples I think
this is in keeping with the intent of the courses.

While the first volume carefully avoided the subject of optimization, this volume
starts with a general but wide-ranging discussion of it. As any optical designer quickly
discovers, the key to this art and science (as Professor Shannon has referred to our field)
is optimization. In fact, a desire to learn more about optimization probably brought many
people to these courses, even some who had been designing lenses for many years. More
specifically, the courses taught "local" optimization, where the choice of starting design is
crucial to the success of the optimized design. Michael was also interested in the more
general problem of "global" optimization, which he somewhat wryly described as a user
inputting a series of "flat plates" and the program finding the best possible arrangement of
lens elements ideally, the program would even decide the optimum number of plates,
mirrors, diffractive elements, and so on.

The first chapter in this volume has been compiled from Michael's writings on local
optimization, from several published papers as well as his course notes. This material is
inevitably very closely related to the Imperial College and Sigma software that he
developed and used. Unfortunately, readers of this book will not have access to Sigma,
or Michael's unique ability to answer questions as they arise. They will instead be using
another commercial optimization program, perhaps without supervision. Recognizing this
inevitable limitation, I have attempted to rise above the trees of the Sigma program and
give my interpretation of Michael's overview of the forest that is any optical design
optimization program, at least one that is based on the damped least squares (DLS)
method.

Included here are some design examples to illustrate certain points, such as the
effects of lens diameter and thickness constraints on aberration performance. In the
courses, these examples were in a separate section under the heading of "unusual or novel
optical designs." One of these is the "monochromatic quartet," which I was fortunate
enough to find with Sigma for the International Lens Design Conference problem in 1990.
Several other designers also found the same form with other local optimization programs,
and the design has subsequently been rediscovered by global optimization from flat plates
but I have been gratified to hear that such programs have not yet found a better design.
Although totally impractical (which was the intention), it is a good illustration of the
importance of size constraints, which is one of the key factors in the control of higher-order
aberrations.

The chapter concludes with the Kingslake double-Gauss example that became a
tradition of Michael's courses. This was the start of the practical work with Sigma, but in
this book readers are left to apply it to whichever optical design program they are using.
Naturally, the detailed lens and ray setup will be quite different from one program to
another. However, the example is retained with Sigma output because this is the way it was
in the courses, and it also serves to illustrate the importance of damping factor and step size
on the ultimate performance of the optimized design. It is unfortunate that in most other
commercial programs these numbers remain invisible to the designer Sigma was a model
of transparency.

Perhaps the most important message from the first chapter, and indeed the whole
book, is the role of higher-order aberration correction in most optical designs.
Accordingly, the second chapter is a relatively brief discussion of Buchdahl fifth-order
aberrations, with references provided for those mathematically inclined readers who want
all the gory details. Over the years, after "graduating" as a formal student of Michael's, I
had several discussions with him about Buchdahl aberrations while I went through a phase
in my career when I was enthusiastic about them. I think he remained rather skeptical, even
though Sigma became one of the few commercial lens design codes that included
Buchdahl's monochromatic aberration coefficients in the main program (other programs
have them as reluctant extensions). This is not only because they cannot simply be
attributed to individual optical surfaces, but also because they are not usually sufficiently
accurate, since they are based on paraxial rays. Michael made the point that it is usually
quicker and always more accurate to trace a limited number of finite rays, and this is
indeed the more common approach in this age of very fast personal computers.
It remains useful to think about fifth- and higher-order aberrations such as oblique
spherical aberration, coma, astigmatism, and field curvature, because these often dominate
the lens design problem. Usually I look for them in the transverse ray aberration plots, of
which there are many examples in these two books. Someone (I forget who) has defined
an optical designer as one who understands transverse ray aberration curves, and so this
is considered a prerequisite for the reader of this intermediate-level text. Later in my
career, thanks to Abe Offner and Juan Rayces, I became a convert to Zernike coefficients,
which more accurately describe and optimize higher-order aberrations. While the last
version of Sigma did contain these coefficients, the original course material contains little
discussion of them, so I have decided not to add that here.

The remaining chapters contain a wide range of design examples that are
dominated by higher-order monochromatic and chromatic aberrations. The choice of
examples partly reflects Michael's background and interest in certain design types, but it
also evolved from student requests. It does not attempt to cover all design types, but
rather it uses these examples to illustrate specific or generally applicable design
approaches.

Many readers may find in the third chapter the most useful insights into an optical
designer's thought processes, such as they are. The synthesis of starting points for
optimization is the aspect of optical design that is the least written about but most
important at least until the truly global optimization program arrives. While there have
been numerous attempts to apply databases and artificial intelligence, here the approach
to the challenge of the blank computer screen is to use human memory, common sense,
experience, and knowledge. It involves using the (local) optimization program as a field in
which to play with new ideas, discarding those that show less promise, and then refining
the more promising ones to include greater accuracy and all of the required practical
aspects prior to finalizing a design for manufacture. To the outsider this may seem like trial
and error, but readers of this book are likely to appreciate that there is more to it than that!
Michael had a particular interest in the history and practice of photography, so the
fourth chapter covers many of the classical photographic lenses. Although these will
already be well known to most readers, this is a brief review, with some valuable insights
and historical observations.

The fifth chapter attempts to cover a wide range of approaches to the problem of
secondary spectrum correction, which is a higher-order chromatic aberration that the
practicing designer will often encounter, and which can be the most stubborn imaging
defect to reduce or eliminate. The most common approach has been to use anomalous
glass types, and this is briefly reviewed. I have also added references to many of the
published systematic methods of glass selection. Some less well known approaches using
normal glasses are also described in more detail, and I have added a brief reference to the
use of diffractive optics, since they are starting to be used in photographic lenses. I have
also added the Schupmann medial telescope, from a prescription kindly provided by
Richard Bingham. This is not often thought of as a means of secondary spectrum
correction, since it avoids the problem rather than corrects it. An implicit lesson of these
two volumes is that avoidance is usually better than correction! Many other catadioptric
designs also use the Schupmann principle, including some described in the last chapter of
Fundamental Optical Design.

Chapter 6 illustrates the wide variety of situations that an optical designer may
encounter, where in this case chromatic aberrations are unimportant, but other
considerations specific to lasers need to be taken into account. Even for the simplest
designs the opportunity is taken to remind us of some basic aberration theory, such as the
sine condition, which was covered in more detail in the first volume.
The material in Chapters 7 and 8 were in the courses combined as a section on
high-numerical-aperture designs. I have separated them into two chapters here, on the
basis that microscope objectives operate over a relatively small field size and broad
spectral bandwidth, whereas microlithographic objectives cover a relatively large field size
and narrow spectral range. No doubt this also reflects my own interest in microlithography,
from where I have added a few more designs some my own with the justification that
the courses did include one of my earlier designs, and I wanted to include the substantial
progress that has taken place since then.
Microlithographic objectives are the best illustration of the remarkably high and
uniform performance across the image format that can be obtained by the combination of
large size and complexity to "relax" the optical design, a term first used by Glatzel in 1980.
Essentially, this strategy simply minimizes ray incidence angles on optical surfaces. It is one
of the more remarkable stories in the history of optics that such large and complex designs
are now routinely produced with aberrations measured in a small number of milliwaves rms
in the ultraviolet spectrum.

Another class of systems that one might more reasonably expect to find in a book
on advanced optical design is zoom lenses. As a designer with little experience in this field,
and one who skips over the numerous complicated papers on such lenses, I found
Michael's course notes on the subject remarkably easy to understand this is the genius
of Michael's teaching style. I have not changed the material significantly from the original,
other than making the tables and graphics compatible with the rest of the book. After
working with this chapter, I felt that I had sufficient understanding of zoom lenses to at least
have the confidence to begin to design one.
Chapter 10 discusses some of the more basic issues involved in the design of tilted
or decentered optical systems. Originally, I was not going to include this chapter, since it
is specific to the particular way that Sigma treated such systems. But, there are some
interesting illustrations here of apparently simple decentered systems with unusual
ambiguities and challenges, which I felt made the chapter of general interest to users of all
optical design programs.

The final chapter is a brief discussion of some of the practical issues involved in
designing a lens that has to be manufactured within specified price and performance
requirements. The original courses also included a more detailed discussion of tolerancing,
using Sigma's methodology. However, I decided not to include that here, since it is rather
too specific to Sigma. The user of another optical design program will generally find
appropriate documentation provided with it, or may have to develop tolerancing methods
for specific applications, but I considered such a discussion to be beyond the scope of this
book.

I have not, for similar reasons, reproduced here other features of Sigma that were
in the original course notes or program documentation. These include nonsequential
raytracing, illumination system design, Gaussian beam propagation, fiber coupling, and so
on.
I have also not provided a list of recommended reading, beyond the references
given in each chapter, which I have expanded considerably from those given in the courses.
However, mention should be made of Don O'Shea's extensive compilation of optical
design papers on CD-ROM.1 This includes, among others, all of Michael Kidger's
published papers from the Proceedings of SPIE.

Many of the design examples in these two volumes were included in Sigma's
optical design database. These have been converted and now form a part of the Zebase
lens database. There may be subtle differences in some of these lens prescriptions, such
as glass refractive index data, apertures, and fields, which the reader is encouraged to
explore; perhaps the prescriptions can be improved, or starting points for new designs can
be formed. This is one reason why the paraxial ray data and Seidel aberration tables have
been included for many of the designs: they can be used to check the accuracy of
translation of the lens prescription into other optical design programs. Study of these tables
is also a good way to understand how a design is working; it is one of the more important
skills of the optical designer. Of particular interest are the marginal and chief ray incidence
angles (A and ABAR), showing how "relaxed" the design is, and the magnitude of surface
aberrations and how they are cancelled within the system. This will affect the magnitude
of residual higher-order aberrations and sensitivity to manufacturing errors, and is the
implicit theme of these two volumes the simple secret, if there is one, of optical design.
I am grateful to a number of colleagues, including Brian Blandford, Tom
Matsuyama, and Juan Rayces, who have read the manuscript and offered comments and
constructive criticism. I am also very grateful for Tina Kidger's constant encouragement
to "get it out there!" My hope is that this book retains as much as possible of Michael
Kidger's original brevity and clarity, and will be a useful and practical resource for students
of classical optical design, for many years to come.